Relaxation of particle-hole type excitation in a Fermi system within the diffusion approximation of kinetic theory for the case of constant diffusion and drift coefficients

The time evolution of the distribution function for a particle-hole excitation in a Fermi system was calculated using the direct numerical solution of a nonlinear diffusion equation in momentum space. A phenomenological expression for calculating the relaxation time of such an excitation to its equilibrium value has been proposed. It is shown that the relaxation time is dependent on both the excitation energy and the mass number.